2025 SSMO Accuracy Round Problems/Problem 3
Problem
Nonnegative real numbers 
and 
satisfy ![\[\frac{\sqrt{x}+13}{y} = \frac{\sqrt{y}+29}{z} = \frac{\sqrt{z} + 46}{x} = 2\]](http://latex.artofproblemsolving.com/5/e/f/5efb565a73ba272461c8e651f42057f2e54531fd.png)
and ![\[\frac{\sqrt{x} + \sqrt{y}+\sqrt{z}}{x+y+z} = \frac{6}{25}.\]](http://latex.artofproblemsolving.com/c/3/c/c3cb7e8a68d444b529aabbfdd5782dbbd9b46f76.png)
Find the value of 
.
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